نتایج جستجو برای: traveling wave solution

تعداد نتایج: 680051  

2008
ZHI-CHENG WANG SHIGUI RUAN

This paper is concerned with entire solutions for bistable reactiondiffusion equations with nonlocal delay in one-dimensional spatial domain. Here the entire solutions are defined in the whole space and for all time t ∈ R. Assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument, we prove the existence of entire solutions whi...

2013
Zhixian Yu Rong Yuan

Abstract. In this paper, we deal with the existence, asymptotic behavior and uniqueness of travelingwaves for nonlocal diffusion systems with delay and global response. We first obtain the existence of traveling wave front by using upperlower solutions method and Schauder’s fixed point theorem for c > c∗ and using a limiting argument for c = c∗. Secondly, we find a priori asymptotic behavior of...

Journal: :SIAM J. Scientific Computing 2003
Shan Zhao Guo-Wei Wei

In this paper, a discrete singular convolution (DSC) algorithm is introduced to solve Fisher’s equation, to which obtaining an accurate and reliable traveling wave solution is a challenging numerical problem. Two novel numerical treatments, a moving frame scheme and a new asymptotic scheme, are designed to overcome the subtle difficulties involved in the numerical solution of Fisher’s equation....

1997
David P. Nicholls

We present a numerical continuation method for traveling wave solutions to the full water wave problem using a spectral collocation discretization. The water wave problem is reformulated in terms of surface variables giving rise to the Zakharov– Craig–Sulem formulation, and traveling waves are studied by introducing a phase velocity vector as a parameter. We follow non-trivial solution branches...

Journal: :international journal of industrial mathematics 0
s. dhawan department of mathematics, dr. b. r. ambedkar national institute of technology jalandhar, india. s. kumar department of mathematics, dr. b. r. ambedkar national institute of technology jalandhar, india.

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modi ed korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

2016
Seyma Tuluce Demiray Hasan Bulut

Abstract: This manuscript focuses attention on new exact solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The extended trial equation method (ETEM), which is one of the analytical methods, has been handled for finding exact solutions of the system of equations for the ion sound wave and...

Journal: :SIAM Journal of Applied Mathematics 1995
Andrew J. Bernoff Rachel Kuske Bernard J. Matkowsky Vladimir A. Volpert

In many problems, e.g., in combustion or solidification, one observes traveling waves that propagate with constant velocity and shape in the x direction, say, are independent of y and z and describe transitions between two equilibrium states, e.g., the burned and the unburned reactants. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves havi...

Journal: :Physical review. E, Statistical, nonlinear, and soft matter physics 2012
Waipot Ngamsaad Kannika Khompurngson

In this paper, we investigated a density-dependent reaction-diffusion equation, u(t)=(u(m))(xx)+u-u(m). This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation, which is widely used in population dynamics, combustion theory, and plasma physics. By employing a suitable transformation, this equation was mapped to the anomalous diffusion equation where th...

1997
Xinfu Chen Xuefeng Wang

The existence, uniqueness, and global exponential stability of traveling wave solutions of a class of nonlinear and nonlocal evolution equations are established. It is assumed that there are two stable equilibria so that a tr aveling wave is a solution that connects them. A basic assumption is the comparison principle: a smaller initial value produces a smaller solution. When applied to di eren...

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